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Analytic solution of transcendental equations

Górecki H.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

671-677

A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.

A new method for analytic determination of extremum of the transients in linear systems

Górecki H.

Control and Cybernetics

2004

Vol. 33, no 2

275-295

The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, because extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems. In this paper a method which permits to determine extremal values of the error in higher-order systems is proposed.